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Positive configurations of flags in a building and limits of positive representations

  • Giuseppe MartoneEmail author
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Abstract

Parreau compactified the Hitchin component of a closed surface S of negative Euler characteristic in such a way that a boundary point corresponds to the projectivized length spectrum of an action of \(\pi _1(S)\) on an \({\mathbb {R}}\)-Euclidean building. In this paper, we use the positivity properties of Hitchin representations introduced by Fock and Goncharov to explicitly describe the geometry of a preferred collection of apartments in the limiting building.

Notes

Acknowledgements

It is a pleasure to thank my thesis advisor, Francis Bonahon, for encouraging me to think about this problem, for the numerous insightful conversations, and for his support. I thank Daniele Alessandrini and Beatrice Pozzetti for useful discussions and feedback. I am very grateful to the referee for providing several useful comments on an earlier version of this manuscript.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of MichiganAnn ArborUSA

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